With a flat mallet, gently pound 4 boned, skinned chicken breast halves (1 1/2 lb. total) between sheets of plastic wrap until they're about 1/4 inch thick in center and 1/8 inch thick around the edges.
Mix 1/2 cup (1/4 lb.) butter or margarine with 2 tablespoons minced parsley and 1 teaspoon each grated lemon peel, dried tarragon, dried thyme, and dried basil. (Or make half this mixture for a dish that's less rich but not quite as impressive.) Peel plastic from chicken and mound equal portions of butter mixture in the centers of breast halves. To shape each breast half, lap a long side of chicken over the butter mixture. Fold narrow ends of chicken toward the center, slightly over butter, making the bundle about 5 1/2 inches long. Lap remaining long side of breast over the first to completely enclose butter. If any butter is exposed, pull a thin edge of breast over it, or tear a bit of chicken from the edge and press it over the opening.
Break 1 large egg into a shallow pan and beat with a fork to blend. Put 1/2 cup fine dried bread crumbs in another shallow pan. Roll each breast half in egg, then in crumbs; place breasts slightly apart on a sheet of waxed paper.
Set a 10- to 12-inch ovenproof frying pan over high heat. Add 1 tablespoon butter or margarine. When butter sizzles, carefully lay crumb-coated chicken breasts side by side in pan. Brown, turning once with a wide spatula, 2 to 3 minutes total. Put in a 400° oven and bake until chicken is an even golden brown, 6 to 8 minutes (about 10 minutes if chilled). Note: You can't cut to test without creating a leak.
Transfer chicken to plates. Season to taste with salt. Serve with steamed diced potatoes (about 2 lb. total) to share butter filling.
Nutritional analysis per serving with potatoes.